Andrew Nystrom Math 250

• • • Where did the word come from?

A book from the year 825 Author is Muhammad Ibn Mūsa Al-Khwārizmī

• • • • From modern-day Uzbekistan Lived in Baghdad Studied at “The House of Wisdom” Wrote many books; “Algebra” most famous

• • “One square, and ten roots of the same, are equal to thirty nine dirhems. That is to say, what must be the square which, when increased by ten of its own roots, amounts to thirty nine?” In other words,

1. Halve the number of roots 2. Multiply it by itself 3. Add it to the LHS 4. Take the root of the resulting sum 5. Subtract half the number of roots 6. Answer!

Essentially, we get

• Write it in the following form: • Then use the quadratic equation: • Then

• Using our method, we get • • • Our method yields both a positive and negative root. Why?

Negative numbers were not recognized during Al-Khwārizmī’s time.

But are his and our formulas really different?

• Basically, his method for solving quadratic equations is • With a little algebra, we can reconcile it to something like our modern version.

• In the 16 th century, Thomas Harriot and René Descartes wrote equations as • Leading to